Covariant theory of asymptotic symmetries, conservation laws and central charges

Abstract

Under suitable assumptions on the boundary conditions, it is shown that there is a bijective correspondence between equivalence classes of asymptotic reducibility parameters and asymptotically conserved n − 2 forms in the context of Lagrangian gauge theories. The asymptotic reducibility parameters can be interpreted as asymptotic Killing vector fields of the background, with asymptotic behaviour determined by a new dynamical condition. A universal formula for asymptotically conserved n − 2 forms in terms of the reducibility parameters is derived. Sufficient conditions for finiteness of the charges built out of the asymptotically conserved n − 2 forms and for the existence of a Lie algebra g among equivalence classes of asymptotic reducibility parameters are given. The representation of g in terms of the charges may be centrally extended. An explicit and covariant formula for the central charges is constructed. They are shown to be 2-cocycles on the Lie algebra g. The general considerations and formulas are applied to electrodynamics, Yang-Mills theory and Einstein gravity.

BMS charge algebra

“…Our starting point is the covariant approach to surface charges and their algebra developed in [10] (see also [11,12]). In particular, for pure Einstein gravity with or without a cosmological constant, it has been shown in [13] that for the linearized theory, described by h µν around a background g µν , the conserved surface charges are completely classified by the Killing vectors ξ µ of the metric g µν .…”

Free boundary conditions and the AdS3/CFT2 correspondence

“…The charges associated with these symmetries may be computed by standard methods [17][18][19][20]. For three-dimensional gravity the infinitesimal charge corresponding to the asymptotic Killing vector ξ is given by…”

Warped AdS3 black holes in higher derivative gravity theories

“…2 Then, exploiting again the symmetries and using the Covariant Phase Formalism [26,27,75,[77][78][79][80] we will be able to compute the charges and central charges appearing in (1.4) and (1.5). In particular, we will find that…”

“…This ambiguity generalizes the one in the symplectic potential (n − 1)-form under Θ → Θ + dY, and hence in the symplectic structure. One proposal to fix this ambiguity [78,79] is by acting on the weakly vanishing Noether current with a contracting homotopy operator, yielding an (n − 2)-form denoted k BB ξ (δΦ, Φ). In essence, this operator is the inverse of the exterior derivative d (see e.g.…”